What is the center 36x^2+288x+64y^2-256y=1472 ?

The center 36x^2+288x+64y^2-256y=1472 is (-4,2)

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center 36x^2+288x+64y^2-256y=1472

center

36 x^{2} + 288 x + 64 y^{2} - 256 y = 1472

(- 4, 2)

Solution steps

36 x^{2} + 288 x + 64 y^{2} - 256 y = 1472

Rewrite

36 x^{2} + 288 x + 64 y^{2} - 256 y = 1472

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{8 ^{2}} + \frac{( y - 2 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, 2), a = 8, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, 2), a = 8, b = 6

And the center is:

(- 4, 2)

16 x^{2} + 25 y^{2} = 400

x^{2} + 4 y^{2} + 7 = 12 y - 2 x

2 x^{2} + y^{2} + 4 x = 4

9 (x - 3)^{2} + (y + 2)^{2} = 18

x^{2} + y^{2} + 4 y = 0

What is the center 36x^2+288x+64y^2-256y=1472 ?
The center 36x^2+288x+64y^2-256y=1472 is (-4,2)